Elastic wave propagation in curved flexible pipes

The elastic wave guide properties of a curved flexible pipe, idealised as a thin walled toroidal shell, are under consideration in this paper. Two mathematical models of such a shell are developed and validated. One model is analytical and is based on classical thin shell theory and the Galerkin's method is being employed. This provides an eigenvalue problem, from which the dispersion relation and the modal vectors are extracted. The other model is numerical and utilises the wave finite element method. By modelling a segment of the toroidal shell in a finite element environment, and exporting the mass and stiffness matrices, another eigenvalue problem is formulated, and the dispersion relation and the modal vectors are extracted. The two models back each other up with respect to validity and reliability. They provide insight about which waves (travelling as well as evanescent), that are supported by the toroidal shell. With this insight, it is possible to identify three regimes of wave motion, a curved beam regime, a cylinder regime, and a torus regime, and to explain the differences between these regimes. The identification of the regimes is based on analysing both dispersion diagrams and mode shapes.